A possibility we have in mind is that the current time value \(|\Omega _{K,0}| \lesssim 10^{-3}\)  derived from the data fitted with the standard model [1]}, i.e. assuming Einstein's equation, might be biased due to the fact that this equation implicitly prefers a Euclidean topology, in the sense that its NR limit is only possible in this type of topology. Therefore, starting from a theory without such a preference, e.g. the present bi-metric theory, might lead to another value of \(\Omega _K\) . If this is the case, the hope is that other parameters might also be changed and some tensions of the current model solved. As an example, let us consider the recent study performed by [2]} (see also e.g. [3]}, ) who showed that the best fit of the CMB power spectrum at all scales seems to prefer a value at current time of \(\Omega _{K,0} \simeq -0.045\)  (equivalently in their case \(\Omega _{K,0} h^2 \simeq -0.013\) , with \(h = H_0/(100 \ \rm {km/s/Mpc})\) ). The main issue with this analysis is that it changes the Hubble constant \(H_0^{\rm CMB}\)  inferred from the CMB, increasing too much the tension with the local supernovae measurement \(H_0^{\rm SNe}\) : from \(H_0^{\rm SNe} - H_0^{\rm CMB} \sim 5\)  km/s/Mpc to \(H_0^{\rm SNe} - H_0^{\rm CMB} \sim 20\)  km/s/Mpc. If their evaluation of the curvature is solely based on the CMB data and does not depend on the expansion model between the CMB time and current time, their value of curvature \(\Omega _{K,0} h^2 \simeq -0.013\)  might still be obtain in our cosmological model from the analysis of the CMB power spectrum alone. However, because in that model curvature does not affect anymore directly the expansion, then from the same initial conditions in terms of matter density \(\Omega _{m, \rm i}\) , redshift \(z_{\rm i}\)  and expansion rate \(H_{\rm i}\)  at CMB time, the Hubble constant at current time is unchanged, keeping the tension at around 5 km/s/Mpc. A hope with the second question is that, on top of providing a best fit of the CMB power spectrum as in the analysis of [2]} with \(\Omega _{K,0} h^2\simeq -0.013\)  while not increasing the Hubble tension, our model would solve it. For this, other cosmological parameters, such as the sound horizon distanceHowever, changing only \(r_{\rm d}\)  is unlikely to solve the Hubble tension as pointed out by ., calculated from the CMB must be changed compared to what is obtained with the standard model.
However, the analysis of the CMB is subtle as pointed out by   who performed a similar study as [2]} of the CMB power spectrum without finding an evidence for a positive spatial curvature. This shows that a complete thorough reevaluation of the cosmological parameters, within the context of our model, using Planck's data (as in [2]}) and/or catalogues of galaxies (as in [7]}) is required to assess whether or not the blind expansion law (REF ) and the weak field equations in Table REF , which were derived for this purpose, can provide a better fit of the data than the standard model. Such a better fit would only be possible if \(\Omega _K\)  is found non-negligible within our model, otherwise, it is equivalent to the standard model.
